Long-Range Dipole-Dipole Interaction and Anomalous F\"{o}rster Energy Transfer across Hyperbolic Meta Material

We study radiative energy transfer between a donor-acceptor pair across a hyperbolic metamaterial slab. We show that similar to a perfect lens a hyperbolic lens allows for giant energy transfer rates. For a realistic realization of a hyperbolic multilayer metamaterial we find an enhancement of up to three orders of magnitude with respect to the transfer rates across a plasmonic silver film of the same size especially for frequencies which coincide with the epsilon-near zero and the epsilonnear pole frequencies. Furthermore, we compare exact results based on the S-matrix method with results obtained from effective medium theory. Our finding of very large dipole-dipole interaction at distances of the order of a wavelength has important consequences for producing radiative heat transfer, quantum entanglement etc.